This assignment is for ETC5521 Assignment 1 by Team Possum comprising of Samuel Lyubic and Yuheng.

1 Introduction and motivation

Volcanoes date back billions of years ago with the first recorded eruption in 1650 BC in Santorini. They are spread out across the globe with many lying along the pacific coast lines along earths tectonic plates. Volcanoes are contributiors to more then 80% of the earths surface which they are able to do through their extreme explosive force and contents, which has led them to have mapped and shaped the the world as it is understood today (https://www.nationalgeographic.com/environment/natural-disasters/volcanoes/). With the force volcanoes are able to generate, they can bring about life however their destructive nature is also understood, and sometimes unfortunately underestimated (https://www.volcanodiscovery.com/volcanic_risk_zones.html#:~:text=For%20instance%2C%20High%20Risk%20Zones,where%20volcanic%20projectiles%20fall%20regularly.&text=With%20bigger%20eruptions%20producing%20heavy,such%20pyroclastic%20flows%20are%20channeled.) with many scientist over the course of history attributing significant changes to the globe and historic climate events to volcanoes, given the range of elements that they emit and as well as the ferocity and magnitude of eruptions (Zeilinski (2015)). As such, the primary question of this report is _“What is the global impact of volcanic eruptions?” in order to better understand the risk volcanoes pose and the ramifications and reverberations to the human population from their eruptions.

2 Data description

The data source is from The Smithsonian Institution, which has been constantly updating since 2013. The data is cleaned and made available for download on (https://github.com/rfordatascience/tidytuesday/blob/master/data/2020/2020-05-12/readme.md), so that we directly import the 5 data sets for this analysis. These 5 data sets are probably the most comprehensive data set around. They are volcano, eruptions, events, tree_rings and sulfur, allowing us to discover the influences among them.

The data source is from The Smithsonian Institution. The data is available, and cleaned, downloadable from tidytuesday github. Cleaning script is also supplied.

Data provided contains 5 linked data sets, each with looking at a particular aspect of volcano:

3 Research questions

4 Analysis and findings

4.1 World Of Active Volcanoes

4.1.1 World Map of Active Volcanoes erupt

Number of eruptions for Primary Volcano Types

Figure 4.1: Number of eruptions for Primary Volcano Types

There are 3 main types of Active Volcanoes namely Stratovolcano, Caldera and Shield. The rest have been labelled as others. Stratovolcanoes are by far the most active volcano.

Active Volcanoes and The Ring of Fire, and Tectonic Plates layourt across the globe

Figure 4.2: Active Volcanoes and The Ring of Fire, and Tectonic Plates layourt across the globe

Figure 4.2 displays two maps, one showing the Active Volcanoes and the ring of fire and the other showing the layour of tectonic plate boundaries.

We found that most of the volcanoes lie along the Pacific Ocean tracing the boundaries of tectonic plates, this is known as the ‘Ring of Fire’ (Society 2019). This path is approximately 40,000km long and holds 75% of the World’s Volcanoes with 90% of them being active. The abundance of volcanoes are explained by significant tectonic plates in the area, as volcanoes are formed through the cracking in the ground created by converging or diverging tectonic plate boundaries.

The Ring of Fire

Figure 4.3: The Ring of Fire

Figure 4.3 displays the Ring Of Fire, which demonstrates the number of volcanoes running along the boundaries. Relatively speaking, the volcanoes here have more eruptions.

4.2 The interaction between volcanoes and humans - what is the range of risk with volcano eruptions?

4.2.1 Population living around active volcanoes

Population within 5, 10, 30, 100km from Volcano

Figure 4.4: Population within 5, 10, 30, 100km from Volcano

Figure 4.4 displays the size of volcanoes as represented by the triangles and their proximity to the nearest population, broken down into 5km, 10km, 30km and 100km.

  • Population size with 5km is mostly less tehn 100
  • However, within a 10km range there is quite a bit of variability in the sizes of the populations in that range.

The impact of a volcano can vary in their destructive nature, creating both immediate and long term risks to the surrounding and global populations. The immediate risk to the surrounding populations come in the physical form of:

  • Pyroclastic flows, which is the extremely hot chaotic mixture of rock fragments, gas, and ash that travels rapidly from an eruption and destroys whats in its path
  • Projectile fragments, fragments of rock that can travel anywhere from 100m to 25km depending on the size and magnitude of the eruption
  • Heavy ash which are clouds consisting of small particles of gases and rocks around the 2mm in size, that are released into the atmosphere and then landing on the ground.

Size of a volcano can be an indicator of the potential damage that could come from an eruption given the positioning and greater velocity that can be prodcued from a larger volcano however, there is no way to create a blanket safe distance rule when it comes to their damage radius is the impact of a volcano uniqely dependent on each individual eruption. Generally, 5-10km range is relatively safe for residincy given the size of most eruptions however, as only an exceptional eruption would result in severe in that range, although these “exceptional eruptions” are not too uncommon for residents who decide to live in this proximity to setup imobile residencies. Volcanic Discovery%20Low%20Risk%20Zone&text=Typically%20you%20are%20more%20than,pyroclastic%20flows%20could%20be%20channeled.)

Figure 4.4 was inspired by Sil Aarts’ visualization where we use geom_polygon to create easy and intuitive visualizations.

4.2.2 World map with number of eruptions in each country

World Map with countries experiencing most eruptions

Figure 4.5: World Map with countries experiencing most eruptions

Figure 4.5 displays the locations of volcanoes with a populations within a 5km radius, with the size of the population mapped to size of the point and orange scale indicating the number of volcano eruptions across the glove. with fill depending on the number of eruptions in each country and larger dot sizes represent the number of population in the vicinity.

  • Most of the countries with higher counts of eruptions lie along the edges of the pacifc ocean, which is known as the “Ring of Fire”
  • The countries along the “Ring of Fire”, specifically Noth America, Chile, Indonesia and Japan have the highest number of populations near the more active volcano sites. Inicating that, living in those countries along the pacific ocean poses a potential higher risk to those individuals relative to those living more inland.[https://www.usgs.gov/faqs/what-ring-fire?qt-news_science_products=0#]

4.3 Is there any relationship between tree rings and volcanic eruption events? (Conducted by Yuheng Cui)

Tree ring is an important indicator to reveal climate and temperature change. tree_rings dataset contains the values of two variables (n_tree and europe_temp_index) from year 0 to year 2000. n_tree is tree ring z-scores relative to year and z-score is a measure of variability from the mean). europe_temp_index is the average yearly temperature for Europe in Celsius relative to 1961 to 1990. We know that tree ring width reflects the growth conditions of the tree — the condition refers to nutrient conditions, precipitation and temperature during a growing season. Seiler, Houlié, and Cherubini (2017) suggest “the ring width may also be influenced by volcanic activity on Mount Etna and in other volcanic regions.” Seiler, Houlié, and Cherubini (2017) also suggest the pre-eruptive phase can only have begun when the trees had already ceased their seasonal growth.

4.3.1 Limitation of tree_ring dataset

tree_ring dataset does not have the accurate tree ring z-score value near the volcanoes, and the temperature index is related to only Europe but not near the active volcanoes. The second limitation is because wildfires also affect the tree ring z-score, but we don’t have the wildfires records of Europe.

Due to tree_ring dataset only containing the temperature index and tree ring data in Europe, we filter the eruption events that occur in Europe only. However, most eruption events were in Russia, and partial Russian territory is belong to Europe. In other words, not all eruptions affect Europe temperature index. But it is still worthy to analyse the relationship between tree rings and volcanic eruption events by using the tree_ring dataset.

4.3.2 Analysis

First, we draw a plot for n_tree and europe_temp_index. Fig 4.6 shows these the changes of two variables along time. The vertical dash lines indicate the eruption events. It seems that two lines generally fit each other. To ensure the correlation between these two variables, we run a correlation test. Table 4.1 shows the estimated correlation is 0.79 and p-value is less than 0.05. This is to say that we are 95% confident that two variables are strongly correlated. Thus, we can build a model for these two variables.

Tree ring z-score and temperature index

Figure 4.6: Tree ring z-score and temperature index

Table 4.1: Correlation test for tree ring z-score and temperature index
estimate statistic p.value parameter conf.low conf.high method alternative
0.7931274 58.20812 0 1998 0.7762827 0.8088402 Pearson’s product-moment correlation two.sided

We build two linear models: \[\large{lm\_1} :\large{\widehat{\text{Europe temp index}}} = 0.1073 + 0.4941 * \text{Tree ring z-score}\]

\[\large{lm\_2} :\large{\widehat{\text{Europe temp index}}} = 0.10765 + 0.49421 * \text{Tree ring z-score} - 0.02598 * \text{Eruption}\] In lm_2, for eruption, 1 means there was an eruption while 0 means none.

Table 4.2 shows the goodness of two models. lm_2 is slightly better than lm_1 because its \(r^2\) is slightly greater than lm_1’s \(r^2\). In conclusion, both of them are not good because of low r_square. For example, lm_1 has \(r^2\) of 0.6287, which means only 62.87% of variation explained by the model. The reason might be an eruption has its radius of influence, and most of the eruptions were in Russia, thus, they did not have big influence in Europe temperature index. In addition, even there was a big eruption, it can hardly affect the whole Europe or the yearly average temperature index.

To visulising the fittness of lm_2, we plot the residual value based on lm_2. Residual value refers to the difference between observed and predicted value. If a model is a good model, the residual value would close to y intercept. Fig @ref(fig:lm_2_resid) shows the residual value spread, and variation of residual value is increasing while the temperature index is more far away from 0. This means, in some degree, lm_2 can predict the europe_temp_index under non-extreme value of n_tree.

Table 4.2: Compare two models
model r_square
lm_1 (no eruption) 0.6288653
lm_2 (eruption) 0.6287130
Residual lm_2

(#fig:lm_2_resid)Residual lm_2

4.4 Can volcano eruptions predict climate change? (Conducted by Sam Lyubic)

The following section will be conducting analysis on volcano eruptions in order to assess how the elements of en eruption may impact the atmosphere and the resulting impact on climate.

As discussed, a volcanic eruption can vary in VEI magnitude and range in the substances that are released however, a constant element that is emitted during eruption is Sulfur, which is subsequently also one of the most effective elements in cooling the climate. When sulfur is released into the stratosphere it combines with water to form sulfuric acid aerosols that produce a coating of small droplets in the upper stratosphere which act as a reflector to incoming solar radiation and result in a global coolng of the earths surface, with the aerosols able to stay in the statrosphere for up to 3 year, eventually falling back to earth. Furthermore, as discussed tree ring scores can be used to act as a proxy in order to understand the weather at the time thus by assessing the linearage of sulfur events and tree ring scores the impact of volcanic eruptions on climate change can be assessed (UCAR (2020)).

The primary variables being used to assess the sulfur levels, in nannograms per gram, in the northern and southern hemisphere across the date range of 500-705 ce are:

  1. NEEM - ice cores from Greenland
  2. WDC - ice cores from Antartica

Given the stable ice sheets as well as the earths rotation and locations of Greenland and Anatartica, the ice sheets abosrb and store the elements released during events in history and the NEEM and WDC team have been able to extract ice sheets that store records of atmospheric concentration of greenhouse gases, surface air temperature. Sulfur being one of these elements, thus the ice cores allow for a construction of a time series of the level of a sulfur at any given year thus allowing a reconstruction of when sulfuric events in the form of eruptions took place (NEEM (2020)) (WAIS (2020)).

The histroic time frame provides critical information on the history of eruptions and sulfuric events thus allowing to better understand what caused certain events in history, such as ice ages and prolonged periods of cooling, and long term effects of sulfuric depositions impact the earth in order to better understand the likey outcome on climate from an eruption and how to plan accordingly. [https://www.researchgate.net/publication/279965759_Timing_and_climate_forcing_of_volcanic_eruptions_for_the_past_2500_years]

Time series of the sulfur events that have been recorded in Greenland and Antartica and the European weather index and Tree Ring Z-Score

Figure 4.7: Time series of the sulfur events that have been recorded in Greenland and Antartica and the European weather index and Tree Ring Z-Score

Figure 4.7 displays three plots with year on the x axis and, for (A) and (B), historically recorded sulfur levels on the y axis while for (C) and (D), percentage change:

  • Plot (A) visualises the recorded sulfur levels, in ng/g, in the extracted Antartic ice sheet from year 500 to 705 CE
    • Plot (B) visualises the recorded sulfur levels, in ng/g, in the extracted Greenland ice sheets from year 500 to 705 CE
    • Plot (C) visualises the change in tree ring score size from year to year
    • Plot (D) visualises the year on end percentage change in european weather index
    • The red line indicating a volcanic eruption impacting the Southern hemisphere
    • The green vertical line indicating a volcanic eruption impacting the northern hemisphere
    • The blue vertical line indicating a bi-polar event impacting both hemispheres.

Looking at plot (A) and (B) the vertical lines indicate sulfuric events that the ice cores recorded and have been attributed to volcanic eruptions. Specifcally:

  • Bipolar events: year 540, 575 and 682
    • Northern Hemisphere events: in year 520, 536, 550, 574 and 627
    • Southern Hemisphere events: in year 683, 690 and 653
    • It is important to note that Northern Hemisphere volcanic eruptions materials tend to stay only in the Northern hemisphere while Southern hemipshere volcanic elements have been found to be move north (Zeilinski (2015)).

All these sulfur depositions have now been attributed to volcanic eruptions at the time (Sigl et al. (2015)) (Zeilinski (2015)). Asessing plot (C) and (D) from Figure 4.7, it is evident that there is negative change and tree growth z scores and climate index that occur after the volcanic eruptions. Specifically:

  • Plot (C) shows an overall trend of drops in tree ring scores after a volcanis eruption and subsequent years of negative of negative tree ring scores.
    • Year 536 saw one of the most significant sulfur depostions from an eruoption in the northern hemisphere with a negative change of -4800% from 0.7 to 3.29.
    • Interestingly, events in 574, 675, 627 and 690 are followed by growth in n tree ring size although still in the negative z score range.

    • However, subsequent years after sulfur events show growth was again negative which indicates the lag and long term impact that sulfur depoistion events have on the stratosphere, as they may not always immediately show an impact however given the length of time the sufur can stay in the stratosphere it shows a long term effect taking place (Sigl et al. (2015)).

    • Plot (D) displays the percentage change of the European temperature index, which displays a relatively negative percentage year on end change in temperature after a volcanic event.
      • Similarly to plot (C), there is a large negative percentage change of -1680% in the year 536 furthermore
      • As the trend in plot (C) show, although in some cases the immediate impact of the volcnic event there is a lagged effect of an overall negative change from year to year in the weather index in the subsequent years after an event.

4.4.1 Correlation test

To supplement the analysis conducted on Figure 4.7, a pearson correlation test was conducted on the tree scores and the yearly average NEEM and WDC sulfur level recordings.

Table 4.3: Tree ring score and yearly mean NEEM correlation test
estimate statistic p.value parameter conf.low conf.high method alternative
-0.3642468 -5.586246 1e-07 204 -0.4771875 -0.2394694 Pearson’s product-moment correlation two.sided
Table 4.4: Tree ring score and yearly mean WDC correlation test
estimate statistic p.value parameter conf.low conf.high method alternative
-0.291919 -4.359315 2.07e-05 204 -0.4121722 -0.1616692 Pearson’s product-moment correlation two.sided

The results from Table 4.3 and Table 4.4 present a negative correlation between the tree ring sizes and the sulfur levels recorded by MEEN and WDC, with: - The correlation between tree rings and MEEN mean sulfur levels: -0.36. - The correlation between tree rings and WDC mean sulfur levels: -0.29.

Thus indicating that with increased sulfur levels tree ring size decreases and given tree rings act as a proxy for weather this leads to the notion that with event of a volcanic eruption taking and the subsequent release of the sulfur gases into the stratosphere there is likely to be both short term and long term climate impact with a global cooling period taking place.

4.5 Which tectonic settings have higher or lower VEI and how this relates to the duration of eruption?

VEI measures the explosiveness of volcanic eruptions which is determined by the volume of contents launched from the eruption. The contents is made up of pyroclastic flow, ash clouds, debrit and rocks with the eruption cloud height and volume being assessed as part of the measure. VEI is qualitatlively described using terms such ranging from “gentle” to “mega-colossal”. [Wikipedia].

Probability density function of eruptions in each VEI category

Figure 4.8: Probability density function of eruptions in each VEI category

Theoretically, VEI ranges from 0 to infinity. In this dataset VEI has been recorded on a log10 scale, thereby each interval (increase of 1 in VEI) indicates an eruption 10x the magnitude. There only bee 40 eruptions over the last 132 million years that recorded a VEI-8 magnitude eruption and only in the last 10,000 years, only 10 eruptions have recorded a VEI-7.

Figure 4.8 presents the number of eruptions for the recorded VEI eruptions since 1812, with the number of eruptions on the x axis and the VEI rating on the y axis. The figure shows:

  • VEI 7 has only one observation since 1812, which occured on Mount Tambora
    • The likelihood of a volcano with VEI 4 or above is very unlikely (less than 1). In fact, almost 98% of all volcanoes have less than VEI-3.
    • Eruptions with a rating of VEI-2 occur relatively more frequently with quite a number of them occurring > 50 times over the time span.

4.5.1 How Frequently do volcanoes erupt?

Frequency of Most Active Volcanoes in each VEI category

Figure 4.9: Frequency of Most Active Volcanoes in each VEI category

Figure 4.9 displays the volcanoes with the largest count of eruptions for each VEI rating presented in Figure 4.8. The frequency of eruptions are shown by the red tiles, with each tile representing an eruption, the year along the x axis with the name of the volcano and the corresponding VEI rating on the y axis.

  • Eruptions with VEI 2 occurred the most frequently, followed by volcanoes with VEI-3.
    • For VEI-4 and above, volcanoes rarely erupted (or erupted prior to 1812) - Kelul-4 was actually an exceptional case as the other VEI-4 volcanoes occurred very seldom.
    • The gentler eruption events occur more frequently while more explosive eruptions are much less frequent.

4.6 What are the ideal settings for eruptions to take place?

The following section will be analysis the duration of eruptions for the range of tectonic settings.

Eruption duration across the range of tectonic settings

Figure 4.11: Eruption duration across the range of tectonic settings

Figure 4.11 displays two figures, one for tectonic settings with long durations - greater then 365 days, and another for short durations - less then 30 days, with the count of the number of eruptions across the range of tectonic plates along the x axis and the tectonic setting on the y axis.

For long eruption durations:

  • Subduction zone / Continental crust ( >25km) has the most erupations with the longest duration, making up 58.82% of the erupations that lasted longer then 365 days. It stands far out in front of the next closest tectonic setting which is Subduction zone / Oceanic crust ( <15km) with 14 recorded long eruptions.
    • The remaining tectonic settings have very close figures, as well as proportions with Intraplate / Intermediate crust (15-25 km) showing to have the least number of long eruptions. For short eruption durations:
    • Similarly to the long duration, Subduction zone / Continential crust (>25km) has by far the largest number of short duration eruptions and Intraplate / Intermediate crust (15-25km) has the least number of short duration eruptions
    • There is variation in the middle order of tectonic settings relative to the long duration figure with only 7 long duration eruptions (4.575%) on Rift zone / Oceanic crust ( <15km), however the number of short duration eruptions rises to 30, accounting for 10.067% among all tectonic settings.

Moreover, comparing the count figures, it is apparent that every number from long duration eruptions for all tectonic settings increase when it comes to short duration thus indicating that short duration eruptions occur more frequently than longer ones.

4.6.1 What are the eruption frequencies associated with the range of tectonic settings?

The following section will be analysing which how frequently each tectonic setting erupts, specifically assessing high frequency counts that involve two or more eruptions per year,

The high or low frequncies associated with the range of tectonic settings

Figure 4.12: The high or low frequncies associated with the range of tectonic settings

Figure 4.12 displays the tectonic settings with the record of at least two or more volcano eruptions within one year with the count along the x axis and the tectonic setting on the y axis. Out of 10 tectonic settings recorded (NAs excluded), only 6 of them are listed under this condition. Tectonic settings with both long and short duration eruptions have all been listed here in regards with high frequency.

  • Subduction zone / Continental crust ( >25km) is again positioned with the most number (21 times) of eruptions of high frequency however, here it’s followed by Intraplate / Oceanic crust ( <15km), where only 7 high and 15 short duration eruptions are marked.
    • Rift zone / Oceanic crust ( <15km) has the least number of eruptions with high frequency.

4.6.2 Discussion on tectonic settings and average VEI

Grouped by 10 tectonic settings (NAs excluded), volcano eruptions on Rift zone / Intermediate crust (15-25 km) have the highest average VEI of 2.667, whereas those located on Intraplate / Oceanic crust ( <15 km) obtain the lowest average VEI of 0.923. Furthermore, as shown by Figure 4.11, despite Subduction zone / Continental crust ( >25km) having most longer ( >365 days) and shorter duration ( <30 days) eruptions occur as well as having the most higher frequency ( ≥ 2 eruptions within 1 year) of eruptions, it does not incur a high average VEI. It instead lies in the middle range among the 10 tectonic settings, with the average VEI of 1.982.

Overall, with the highest VEI average (2.667), neither long duration eruptions ( >365 days), nor high frequency (≥ 2 eruptions in 1 year) eruptions are found in Rift zone / Intermediate crust (15-25 km), while only one eruption of short duration ( <30 days) occurs in this setting. On the opposite, with the lowest ranking for average VEI (0.923), volcanoes on the Intraplate / Oceanic crust ( <15 km) don’t tend to erupt with long duration ( >365 days) where it’s long duration eruption only holds 4.575%, compared with other tectonic settings. Nevertheless, it has a greater percentage for both short duration (5.033%) and high frequency (9.677%) eruptions.

Table 4.6: Average VEI level for each tectonic setting
tectonic_settings Avg vei
Rift zone / Intermediate crust (15-25 km) 2.667
Intraplate / Continental crust (>25 km) 2.250
Subduction zone / Intermediate crust (15-25 km) 2.195
Rift zone / Oceanic crust (< 15 km) 2.132
Intraplate / Intermediate crust (15-25 km) 2.091
Subduction zone / Continental crust (>25 km) 1.982
Subduction zone / Oceanic crust (< 15 km) 1.796
Rift zone / Continental crust (>25 km) 1.714
Subduction zone / Crustal thickness unknown 1.623
Intraplate / Oceanic crust (< 15 km) 0.923

5 Conclusion

It is evident from the analysis conducted that volcanic eruptions have a signifcant impact both to local populations and globally. From the analysis conducted it is evident that volcanoes can be unpredictable in VEI magnitude which leads to the notion that there is no blanket range that can followed to the letter that would be deemed safe or unsafe however, for the most part between 5km and 10km range would be considered safe in a mobile home setup. Despite the unpredictabiltiy on a case by case basis of each eruption it would be safest to not populate areas around volcanoes with the tectonic settings of Subduction zone / Continental crust ( >25km) Rift zone / Oceanic crust ( <15km) as these settings are ideal for eruptions and produce a larger number of eruptions, while it would be considered safest to populate areas along Intraplate / Intermediate crust (15-25km) as they tend to be associated with volcanoes that errupt the least frequently with lowest VEI.

Furthremore, by assessing the correlation relationship between tree rings and volcano eruptions, it clear that a strong correlation exits between tree ring z-score and temperature index. But, due to the limitations of tree_ring dataset, we cannot build a good model for temperature index. The model (lm_2) can only predict the temperature index well except for extreme values of weather index. To build a better model, we need more accurate temperature index around volcanoes. Following on, Figure 4.7 displays the percentage change in european weather index and tree ring size with the differing levels of sulfur recorded with a negative correlation exsiting between tree ring score sizes and both yearly mean MEEN and WDC sulfur levels inficating that after a volcanic eruption there is likely to be a subsequent period of cooling and climate change, showing the critical impact that volcano eruptions have both locally and globally.

Acknowledgements

Data source is from Institution (n.d.).

In order to map the tectonic boundaries the tectonic plates were split at the prime meridian (x-intercept where long = 0) with the assistiance of Z.Lin at StackOverflow. The datasets were joined with the world map datasets provided by ggplot to find the continent and country coordinates as well as dataset from Kaggle to obtain coordinates to plot the tectonic plates polygon.

These packages are used to produce this report:

tidyverse (Wickham et al. 2019), lubridate (Grolemund and Wickham 2011), broom (Robinson, Hayes, and Couch 2020), leaflet (Cheng, Karambelkar, and Xie 2019), ggmap (Kahle and Wickham 2013), mapview(Appelhans et al. 2020), viridis (Garnier 2018), rgdal (Bivand, Keitt, and Rowlingson 2020), kableExtra (Zhu 2020), gridExtra (Auguie 2017), readr (Wickham, Hester, and Francois 2018), knitr (Xie 2014), sf (Pebesma 2018), data.table (Dowle and Srinivasan 2020), ggthemes (Arnold 2019), maps (Richard A. Becker, Ray Brownrigg. Enhancements by Thomas P Minka, and Deckmyn. 2018), ggridges (Wilke 2020), rvest (Wickham 2020)

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